Question 1

If a decision variable is not positive in the optimal solution, its reduced cost is

Accepted Answer

A)  what its objective function value would need to be before it could become positive. 
B)  the amount its objective function value would need to improve before it could become positive. 
C)  zero. 
D)  its dual price. 
A)  what its objective function value would need to be before it could become positive. 
B)  the amount its objective function value would need to improve before it could become positive. 
C)  zero. 
D)  its dual price. B

Question 2

If the dual price for the right-hand side of a ≤ constraint is zero, there is no upper limit on its range of feasibility.

Accepted Answer

A) True 
 B)False  True

Question 3

In order to tell the impact of a change in a constraint coefficient, the change must be made and then the model resolved.

Accepted Answer

A) True 
 B)False  True

Question 4

In a linear programming problem, the binding constraints for the optimal solution are
5X + 3Y ≤ 30
2X + 5Y ≤ 20
a.Fill in the blanks in the following sentence:As long as the slope of the objective function stays between _______ and _______, the current optimal solution point will remain optimal.
b.Which of these objective functions will lead to the same optimal solution?1) 2X + 1Y 2) 7X + 8Y 3) 80X + 60Y 4) 25X + 35Y

Accepted Answer

a.−5/3 and −2/5
B.Ob

Question 5

Which of the following is not a question answered by standard sensitivity analysis information?

Accepted Answer

A)  If the right-hand side value of a constraint changes, will the objective function value change? 
B)  Over what range can a constraint's right-hand side value without the constraint's dual price possibly changing? 
C)  By how much will the objective function value change if the right-hand side value of a constraint changes beyond the range of feasibility? 
D)  By how much will the objective function value change if a decision variable's coefficient in the objective function changes within the range of optimality? 
A)  If the right-hand side value of a constraint changes, will the objective function value change? 
B)  Over what range can a constraint's right-hand side value without the constraint's dual price possibly changing? 
C)  By how much will the objective function value change if the right-hand side value of a constraint changes beyond the range of feasibility? 
D)  By how much will the objective function value change if a decision variable's coefficient in the objective function changes within the range of optimality?

Question 6

The dual price associated with a constraint is the change in the value of the solution per unit decrease in the right-hand side of the constraint.

Accepted Answer

A) True 
 B)False

Question 7

​Explain the connection between reduced costs and the range of optimality, and between dual prices and the range of
feasibility.

Accepted Answer

In the context of linear programming (LP

Question 8

An objective function reflects the relevant cost of labor hours used in production rather than treating them as a sunk cost. The correct interpretation of the dual price associated with the labor hours constraint is

Accepted Answer

A)  the maximum premium (say for overtime) over the normal price that the company would be willing to pay. 
B)  the upper limit on the total hourly wage the company would pay. 
C)  the reduction in hours that could be sustained before the solution would change. 
D)  the number of hours by which the right-hand side can change before there is a change in the solution point. 
A)  the maximum premium (say for overtime) over the normal price that the company would be willing to pay. 
B)  the upper limit on the total hourly wage the company would pay. 
C)  the reduction in hours that could be sustained before the solution would change. 
D)  the number of hours by which the right-hand side can change before there is a change in the solution point.

Question 9

When the right-hand sides of two constraints are each increased by one unit, the objective function value will be adjusted by the sum of the constraints' dual prices.

Accepted Answer

A) True 
 B)False

Question 10

If the range of feasibility for b1 is between 16 and 37, then if b1 = 22 the optimal solution will not change from the original optimal solution.

Accepted Answer

A) True 
 B)False

Question 11

For any constraint, either its slack/surplus value must be zero or its dual price must be zero.

Accepted Answer

A) True 
 B)False

Question 12

​Sensitivity analysis is concerned with how certain changes affect

Accepted Answer

A)  ​the feasible solution. 
B)  ​the unconstrained solution. 
C)  ​the optimal solution. 
D)  ​the degenerative solution. 
A)  ​the feasible solution. 
B)  ​the unconstrained solution. 
C)  ​the optimal solution. 
D)  ​the degenerative solution.

Question 13

Relevant costs should be reflected in the objective function, but sunk costs should not.

Accepted Answer

A) True 
 B)False

Question 14

​A cost that is incurred no matter what values the decision variables assume is

Accepted Answer

A)  ​a reduced cost. 
B)  ​an optimal cost. 
C)  ​a sunk cost. 
D)  ​a dual cost. 
A)  ​a reduced cost. 
B)  ​an optimal cost. 
C)  ​a sunk cost. 
D)  ​a dual cost.

Question 15

​How is sensitivity analysis used in linear programming? Given an example of what type of questions that can be
answered.

Accepted Answer

Sensitivity analysis is used in linear p

Question 16

The range of feasibility measures

Accepted Answer

A)  the right-hand-side values for which the objective function value will not change. 
B)  the right-hand-side values for which the values of the decision variables will not change. 
C)  the right-hand-side values for which the dual prices will not change. 
D)  each of these choices are true. 
A)  the right-hand-side values for which the objective function value will not change. 
B)  the right-hand-side values for which the values of the decision variables will not change. 
C)  the right-hand-side values for which the dual prices will not change. 
D)  each of these choices are true.

Question 17

The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the

Accepted Answer

A)  optimal solution. 
B)  dual solution. 
C)  range of optimality. 
D)  range of feasibility. 
A)  optimal solution. 
B)  dual solution. 
C)  range of optimality. 
D)  range of feasibility.

Question 18

Classical sensitivity analysis provides no information about changes resulting from a change in the coefficient of a variable in a constraint.

Accepted Answer

A) True 
 B)False

Question 19

When the cost of a resource is sunk, then the dual price can be interpreted as the

Accepted Answer

A)  minimum amount the firm should be willing to pay for one additional unit of the resource. 
B)  maximum amount the firm should be willing to pay for one additional unit of the resource. 
C)  minimum amount the firm should be willing to pay for multiple additional units of the resource. 
D)  maximum amount the firm should be willing to pay for multiple additional units of the resource. 
A)  minimum amount the firm should be willing to pay for one additional unit of the resource. 
B)  maximum amount the firm should be willing to pay for one additional unit of the resource. 
C)  minimum amount the firm should be willing to pay for multiple additional units of the resource. 
D)  maximum amount the firm should be willing to pay for multiple additional units of the resource.

Question 20

The reduced cost for a positive decision variable is 0.

Accepted Answer

A) True 
 B)False

If a decision variable is not positive in the optimal solution, its reduced cost is

If the dual price for the right-hand side of a ≤ constraint is zero, there is no upper limit on its range of feasibility.

In order to tell the impact of a change in a constraint coefficient, the change must be made and then the model resolved.

Which of the following is not a question answered by standard sensitivity analysis information?

The dual price associated with a constraint is the change in the value of the solution per unit decrease in the right-hand side of the constraint.

Explain the connection between reduced costs and the range of optimality, and between dual prices and the range of feasibility.

An objective function reflects the relevant cost of labor hours used in production rather than treating them as a sunk cost. The correct interpretation of the dual price associated with the labor hours constraint is

When the right-hand sides of two constraints are each increased by one unit, the objective function value will be adjusted by the sum of the constraints' dual prices.

If the range of feasibility for b₁ is between 16 and 37, then if b₁ = 22 the optimal solution will not change from the original optimal solution.

For any constraint, either its slack/surplus value must be zero or its dual price must be zero.

Sensitivity analysis is concerned with how certain changes affect

Relevant costs should be reflected in the objective function, but sunk costs should not.

A cost that is incurred no matter what values the decision variables assume is

How is sensitivity analysis used in linear programming? Given an example of what type of questions that can be answered.

The range of feasibility measures

The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the

Classical sensitivity analysis provides no information about changes resulting from a change in the coefficient of a variable in a constraint.

When the cost of a resource is sunk, then the dual price can be interpreted as the

The reduced cost for a positive decision variable is 0.

Introduction

An Introduction to Linear Programming

Linear Programming Applications in Marketing, Finance, and Operations Management

Advanced Linear Programming Applications

Distribution and Network Models

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Time Series Analysis and Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

Exam 3: Linear Programming: Sensitivity Analysis and Interpretation of Solution

If a decision variable is not positive in the optimal solution, its reduced cost is

If the dual price for the right-hand side of a ≤ constraint is zero, there is no upper limit on its range of feasibility.

In order to tell the impact of a change in a constraint coefficient, the change must be made and then the model resolved.

Which of the following is not a question answered by standard sensitivity analysis information?

The dual price associated with a constraint is the change in the value of the solution per unit decrease in the right-hand side of the constraint.

​Explain the connection between reduced costs and the range of optimality, and between dual prices and the range of feasibility.

An objective function reflects the relevant cost of labor hours used in production rather than treating them as a sunk cost. The correct interpretation of the dual price associated with the labor hours constraint is

When the right-hand sides of two constraints are each increased by one unit, the objective function value will be adjusted by the sum of the constraints' dual prices.

If the range of feasibility for b1 is between 16 and 37, then if b1 = 22 the optimal solution will not change from the original optimal solution.

For any constraint, either its slack/surplus value must be zero or its dual price must be zero.

​Sensitivity analysis is concerned with how certain changes affect

Relevant costs should be reflected in the objective function, but sunk costs should not.

​A cost that is incurred no matter what values the decision variables assume is

​How is sensitivity analysis used in linear programming? Given an example of what type of questions that can be answered.

The range of feasibility measures

The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the

Classical sensitivity analysis provides no information about changes resulting from a change in the coefficient of a variable in a constraint.

When the cost of a resource is sunk, then the dual price can be interpreted as the

The reduced cost for a positive decision variable is 0.

Introduction

An Introduction to Linear Programming

Linear Programming Applications in Marketing, Finance, and Operations Management

Advanced Linear Programming Applications

Distribution and Network Models

Integer Linear Programming

Nonlinear Optimization Models

Project Scheduling: Pertcpm

Inventory Models

Waiting Line Models

Simulation

Decision Analysis

Multicriteria Decisions

Time Series Analysis and Forecasting

Markov Processes

Linear Programming: Simplex Method

Simplex-Based Sensitivity Analysis and Duality

Solution Procedures for Transportation and Assignment Problems

Minimal Spanning Tree

Dynamic Programming

Filters

Explain the connection between reduced costs and the range of optimality, and between dual prices and the range of feasibility.

If the range of feasibility for b₁ is between 16 and 37, then if b₁ = 22 the optimal solution will not change from the original optimal solution.

Sensitivity analysis is concerned with how certain changes affect

A cost that is incurred no matter what values the decision variables assume is

How is sensitivity analysis used in linear programming? Given an example of what type of questions that can be answered.